Finite Group Databasebeta

← #11069160

Subgroups — #11069160

Order 768.

2484 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5719C212yesmaximal, complemented
2C3×#2541C211yesmaximal, characteristic, complemented
3#83192C211yesmaximal, characteristic, complemented
4#83176C212yesmaximal, complemented
5#83173C211yesmaximal, characteristic, complemented
6#82705C212yesmaximal, complemented
7#82667C212yesmaximal, complemented
8#82664C212yesmaximal, complemented
9#82644C212yesmaximal, complemented
10C4×#938C211yesmaximal, characteristic, complemented
11D4×C4⋊Dic3C211yesmaximal, characteristic, complemented
12#76725C214yesmaximal, complemented
13#76710C214yesmaximal, complemented
14#76458C212yesmaximal, complemented
15#76324C212yesmaximal, complemented
16#73753C211yesmaximal, characteristic, complemented
17#73716C211yesmaximal, characteristic, complemented
18#39352—31nomaximal, Sylow
19C2×C3×#127C2212yes—
20C2×C3×#127C2211yescharacteristic
21C2×C3×#121C2212yes—
22C2×C3×#121C2212yes—
23C2×C3×C4×D4C2211yescharacteristic
24C2×#939C2214yes—
25C2×#939C2214yes—
26C2×#938C2212yes—
27C2×#938C2212yes—
28C2×#938C2212yes—
29C2×#938C2211yescharacteristic
30C2×#935C2214yes—
31C2×#935C2214yes—
32C2×#935C2214yes—
33C2×D4×Dic3C2212yes—
34C2×D4×Dic3C2212yes—
35C2×D4×Dic3C2212yes—
36C2×C4×#67C2212yes—
37C22×C4⋊Dic3C2212yes—
38#5719—216no—
39C2×#872C2212yes—
40C2×C42×D3C2211yescharacteristic
41C2×#870C2212yes—
42C3×#392C2214yes—
43C3×#390C2212yes—
44C3×C4×C4⋊C4C2211yescharacteristic
45#5222C2214yes—
46#5222C2214yes—
47#5221C2212yes—
48#5221C2212yes—
49#5221C2212yes—
50#5221C2212yes—
51#5221C2212yes—
52#5221C2211yescharacteristic
53#5220C2214yes—
54#5220C2214yes—
55#5212C2212yes—
56C4×#217C2212yes—
57#4987C2211yescharacteristic
58#4987C2211yescharacteristic
59#4987C2211yescharacteristic
60#4984C2212yes—
61#4975C2211yescharacteristic
62#4975C2211yescharacteristic
63#4975C2212yes—
64#4972C2212yes—
65#4972C2211yescharacteristic
66#4961C2214yes—
67#4959C2214yes—
68#4956C2212yes—
69#4952C2214yes—
70#4950C2214yes—
71#4949C2214yes—
72#4949C2214yes—
73#4948C2214yes—
74#4946C2214yes—
75#4944C2212yes—
76#4942C2214yes—
77#4935C2211yescharacteristic
78C4×C4⋊Dic3C2211yescharacteristic
79C4×C4⋊Dic3C2211yescharacteristic
80C4×Dic3⋊C4C2212yes—
81#4928C2212yes—
82#4667C2212yes—
83#4657C2214yes—
84#4650C2212yes—
85C2×#540—32no—
86#2856—31no—
87#2706—34no—
88#2671—34no—
89#2624—32no—
90#2552—31no—
91#2541D311yescharacteristic, complemented
92#2537—32no—
93#2501—32no—
94#2454—32no—
95#2445—32no—
96#2422—32no—
97#2416—32no—
98#2366—31no—
99D4×C4⋊C4—31no—
100C4×#121—31no—
101#2285—31no—
102C22×C3×D4C2312yes—
103C22×C3×D4C2312yes—
104C22×C3×D4C2311yescharacteristic
105C22×C3×D4C2312yes—
106C22×C3×D4C2314yes—
107C22×C3×D4C2314yes—
108C23×C3×C4C2312yes—
109C22×#67C2314yes—
110C22×#67C2312yes—
111C23×Dic3C2314yes—
112C23×Dic3C2314yes—
113C22×C4×D3C2311yescharacteristic
114C22×C4×D3C2311yescharacteristic
115C22×C4×D3C2311yescharacteristic
116C3×#127—28no—
117C3×#127—24no—
118C3×#121—44no—
119C3×#121—44no—
120C3×C4×D4—24no—
121C2×C3×C4⋊C4C2311yescharacteristic
122C2×C3×C4⋊C4C2311yescharacteristic
123C2×C3×C4⋊C4C2311yescharacteristic
124C2×C3×C22⋊C4C2312yes—
125C2×C3×C22⋊C4C2314yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C42C2312yes—
128C2×C3×C42C2311yescharacteristic
129C2×#217C2314yes—
130C2×#217C2314yes—
131C2×#217C2314yes—
132C2×#217C2314yes—
133C2×#217C2312yes—
134C2×#217C2314yes—
135C2×#217C2312yes—
136C2×#217C2314yes—
137C2×#217C2314yes—
138C2×#217C2312yes—
139#939—216no—
140#939—216no—
141#938—28no—
142#938—44no—
143#938—44no—
144#938D418yescomplemented
145#935—216no—
146#935—216no—
147#935—48no—
148D4×Dic3—28no—
149D4×Dic3—28no—
150D4×Dic3—44no—
151C4×#67—44no—
152C2×(C2×D3)⋊C4C2312yes—
153C2×(C2×D3)⋊C4C2312yes—
154C2×(C2×D3)⋊C4C2312yes—
155C2×C4⋊Dic3—44no—
156C2×C4⋊Dic3C2311yescharacteristic
157C2×C4⋊Dic3C2312yes—
158C2×C4⋊Dic3C2311yescharacteristic
159C2×C4⋊Dic3C2311yescharacteristic
160C2×C4⋊Dic3C2312yes—
161C2×C4⋊Dic3C2312yes—
162C2×C4⋊Dic3C2314yes—
163C2×C4⋊Dic3C2311yescharacteristic
164C2×Dic3⋊C4C2312yes—
165C2×Dic3⋊C4C2312yes—
166C2×Dic3⋊C4C2314yes—
167C2×Dic3⋊C4C2314yes—
168C2×Dic3⋊C4C2312yes—
169C2×Dic3⋊C4C2314yes—
170C2×Dic3⋊C4C2312yes—
171C2×Dic3⋊C4C2312yes—
172C2×C4×Dic3C2311yescharacteristic
173C2×C4×Dic3C2311yescharacteristic
174C2×C4×Dic3C2312yes—
175C2×C4×Dic3C2312yes—
176C2×C4×Dic3C2311yescharacteristic
177#872—28no—
178C42×D3—24no—
179#870—28no—
180C3×#95C2312yes—
181C3⋊#95C2312yes—
182C3⋊#95C2312yes—
183C3⋊#95C2312yes—
184C3⋊#95C2312yes—
185C3⋊#95C2314yes—
186C3⋊#95C2314yes—
187C3⋊#95C2312yes—
188C3⋊#95C2312yes—
189#540—616no—
190C2×#127C2×D311yescharacteristic
191C2×#127C2×D312yes—
192C2×#125—32no—
193C2×#123—34no—
194C2×#123—34no—
195C2×#123—34no—
196C2×#121—31no—
197C2×#121—32no—
198C2×#121—34no—
199C2×#121—34no—
200C2×#121—32no—
201C2×#121—32no—
202C2×#121C2×D312yes—
203C2×#121C2×D312yes—
204C2×C4×D4—32no—
205C2×C4×D4—32no—
206C2×C4×D4—32no—
207C2×C4×D4—32no—
208C2×C4×D4C2×D311yescharacteristic
209C2×#117—32no—
210C22×C4⋊C4—32no—
211C22×C42—31no—
212#399—34no—
213#399—34no—
214#398—34no—
215#397—34no—
216#396—34no—
217#394—34no—
218#394—34no—
219#394—34no—
220#394—34no—
221#392C2×D314yes—
222#390—32no—
223#390—32no—
224#390—32no—
225#390—32no—
226#390—32no—
227#390—31no—
228#390C2×D312yes—
229#389—32no—
230#389—32no—
231#389—31no—
232#389—32no—
233#388—32no—
234#386—34no—
235#386—34no—
236#386—32no—
237#385—34no—
238#385—34no—
239#384—31no—
240#384—31no—
241#384—32no—
242#384—31no—
243#382—32no—
244#380—32no—
245#380—31no—
246#380—31no—
247#380—31no—
248#380—34no—
249#380—32no—
250C4×C4⋊C4—31no—
251C4×C4⋊C4—31no—
252C4×C4⋊C4—32no—
253C4×C4⋊C4C2×D311yescharacteristic
254C4×C22⋊C4—32no—
255C24×C3C2414yes—
256C24×C3C2412yes—
257C23×D3C2411yescharacteristic
258C2×C3×D4—28no—
259C2×C3×D4—28no—
260C2×C3×D4—24no—
261C2×C3×D4—22no—
262C2×C3×D4—24no—
263C2×C3×D4—24no—
264C2×C3×D4—24no—
265C2×C3×D4—24no—
266C2×C3×D4—24no—
267C2×C3×D4—22no—
268C2×C3×D4—24no—
269C2×C3×D4—44no—
270C2×C3×D4—42no—
271C2×C3×D4—44no—
272C2×C3×D4—44no—
273C2×C3×D4—42no—
274C2×C3×D4—44no—
275C2×C3×D4C2×D414yes—
276C22×C3×C4—24no—
277C22×C3×C4—24no—
278C22×C3×C4—24no—
279C22×C3×C4C2412yes—
280C22×C3×C4C2412yes—
281C22×C3×C4C2412yes—
282C22×C3×C4C2411yescharacteristic
283C22×C3×C4C2411yescharacteristic
284C22×C3×C4C2411yescharacteristic
285C2×#67—28no—
286C2×#67—42no—
287C2×#67—42no—
288C2×#67—44no—
289C2×#67—44no—
290C2×#67C2×D418yes—
291C22×Dic3—28no—
292C22×Dic3—28no—
293C22×Dic3—44no—
294C22×Dic3—44no—
295C22×Dic3—44no—
296C22×Dic3—44no—
297C22×Dic3C2411yescharacteristic
298C22×Dic3C2412yes—
299C22×Dic3C2412yes—
300C22×Dic3C2412yes—
301C22×Dic3C2414yes—
302C22×Dic3C2411yescharacteristic
303C22×Dic3C2412yes—
304C22×Dic3C2411yescharacteristic
305C2×C4×D3—22no—
306C2×C4×D3—22no—
307C2×C4×D3—22no—
308C2×C4×D3—22no—
309C2×C4×D3—22no—
310C2×C4×D3—22no—
311C2×C4×D3—22no—
312C2×C4×D3—41no—
313C2×C4×D3C2×D414yes—
314C3×C4⋊C4—22no—
315C3×C4⋊C4—22no—
316C3×C4⋊C4—22no—
317C3×C22⋊C4—24no—
318C3×C22⋊C4—44no—
319C3×C22⋊C4—44no—
320C3×C42—24no—
321C3×C42#4114yes—
322#217—28no—
323#217—28no—
324#217—28no—
325#217—24no—
326#217—28no—
327#217—42no—
328#217—44no—
329#217—44no—
330#217—44no—
331#217C2×D418yes—
332(C2×D3)⋊C4—24no—
333(C2×D3)⋊C4—24no—
334(C2×D3)⋊C4—42no—
335C4⋊Dic3—24no—
336C4⋊Dic3—22no—
337C4⋊Dic3—24no—
338C4⋊Dic3—22no—
339C4⋊Dic3—22no—
340C4⋊Dic3—44no—
341C4⋊Dic3—42no—
342C4⋊Dic3C2×D414yes—
343Dic3⋊C4—28no—
344Dic3⋊C4—28no—
345Dic3⋊C4—24no—
346Dic3⋊C4—24no—
347Dic3⋊C4—24no—
348Dic3⋊C4—42no—
349Dic3⋊C4—42no—
350Dic3⋊C4—44no—
351C4×Dic3—24no—
352C4×Dic3—22no—
353C4×Dic3—22no—
354C4×Dic3—22no—
355C4×Dic3—24no—
356C22×D4—32no—
357C22×D4—34no—
358C22×D4C22×D312yes—
359C22×D4C22×D312yes—
360C22×D4C22×D311yescharacteristic
361C22×D4C22×D314yes—
362C22×D4C22×D314yes—
363C22×D4C22×D312yes—
364C23×C4—31no—
365C23×C4—34no—
366C23×C4—34no—
367C23×C4—31no—
368C23×C4—31no—
369C23×C4C22×D312yes—
370#127—28no—
371#127—24no—
372#125—68no—
373#123—616no—
374#123—616no—
375#123—128no—
376#121—38no—
377#121—44no—
378#121—44no—
379#121—68no—
380#121—616no—
381#121—616no—
382#121—124no—
383#121—124no—
384C4×D4—24no—
385C4×D4—68no—
386C4×D4—68no—
387C4×D4—124no—
388C4×D4—124no—
389#117—68no—
390C2×C4⋊C4—31no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—32no—
393C2×C4⋊C4—32no—
394C2×C4⋊C4—32no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—32no—
397C2×C4⋊C4—34no—
398C2×C4⋊C4—34no—
399C2×C4⋊C4—32no—
400C2×C4⋊C4—31no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—32no—
403C2×C4⋊C4—32no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—32no—
406C2×C4⋊C4—124no—
407C2×C4⋊C4C22×D311yescharacteristic
408C2×C4⋊C4C22×D311yescharacteristic
409C2×C4⋊C4C22×D311yescharacteristic
410C2×C22⋊C4—32no—
411C2×C22⋊C4—34no—
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—32no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4—32no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—32no—
423C2×C22⋊C4C22×D312yes—
424C2×C22⋊C4C22×D314yes—
425C2×C22⋊C4C22×D314yes—
426C2×C42—32no—
427C2×C42—32no—
428C2×C42—31no—
429C2×C42—31no—
430C2×C42—31no—
431C2×C42—64no—
432C2×C42C22×D312yes—
433C2×C42C22×D311yescharacteristic
434#95—32no—
435#95—32no—
436#95—32no—
437#95—32no—
438#95—32no—
439#95—32no—
440#95—34no—
441#95—34no—
442#95C22×D312yes—
443C23×C3—22no—
444C23×C3—22no—
445C23×C3—22no—
446C23×C3—22no—
447C23×C3—22no—
448C23×C3—22no—
449C23×C3—24no—
450C23×C3—24no—
451C23×C3—24no—
452C23×C3—24no—
453C23×C3—24no—
454C23×C3—24no—
455C23×C3—24no—
456C23×C3C22×D414yes—
457C23×C3C2511yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3—21no—
463C22×D3—21no—
464C22×D3C22×D412yes—
465C3×D4—28no—
466C3×D4—48no—
467C3×D4—48no—
468C3×D4—84no—
469C3×D4—88no—
470C3×D4—88no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
475C2×C3×C4—22no—
476C2×C3×C4—22no—
477C2×C3×C4—22no—
478C2×C3×C4—22no—
479C2×C3×C4—22no—
480C2×C3×C4—22no—
481C2×C3×C4—22no—
482C2×C3×C4—48no—
483C2×C3×C4C22×D412yes—
484C2×C3×C4C2×#4112yes—
485C2×C3×C4C2×#4112yes—
486C2×C3×C4C2×#4112yes—
487C2×C3×C4H(5,𝔽2)12yes—
488C2×C3×C4H(5,𝔽2)12yes—
489C2×C3×C42−1+412yes—
490#67—48no—
491#67—88no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—22no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—22no—
498C2×Dic3—22no—
499C2×Dic3—22no—
500C2×Dic3—24no—
501C2×Dic3—21no—
502C2×Dic3—22no—
503C2×Dic3—22no—
504C2×Dic3—22no—
505C2×Dic3—21no—
506C2×Dic3—24no—
507C2×Dic3—22no—
508C2×Dic3—24no—
509C2×Dic3—22no—
510C2×Dic3—21no—
511C2×Dic3—22no—
512C2×Dic3—22no—
513C2×Dic3—88no—
514C2×Dic3—88no—
515C2×Dic3C22×D414yes—
516C2×Dic3C22×D412yes—
517C2×Dic3H(5,𝔽2)12yes—
518C4×D3—28no—
519C4×D3—44no—
520C4×D3—44no—
521C24—31no—
522C24C23×D314yes—
523C24C23×D312yes—
524C2×D4—28no—
525C2×D4—28no—
526C2×D4—24no—
527C2×D4—22no—
528C2×D4—24no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—24no—
532C2×D4—24no—
533C2×D4—22no—
534C2×D4—24no—
535C2×D4—38no—
536C2×D4—44no—
537C2×D4—44no—
538C2×D4—42no—
539C2×D4—44no—
540C2×D4—42no—
541C2×D4—44no—
542C2×D4—68no—
543C2×D4—122no—
544C2×D4—122no—
545C2×D4—124no—
546C2×D4—124no—
547C2×D4D3×D414yes—
548C22×C4—24no—
549C22×C4—24no—
550C22×C4—24no—
551C22×C4—31no—
552C22×C4—31no—
553C22×C4—32no—
554C22×C4—34no—
555C22×C4—31no—
556C22×C4—32no—
557C22×C4—32no—
558C22×C4—32no—
559C22×C4—34no—
560C22×C4—62no—
561C22×C4—68no—
562C22×C4—62no—
563C22×C4—62no—
564C22×C4—68no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—62no—
568C22×C4—62no—
569C22×C4—121no—
570C22×C4—124no—
571C22×C4—124no—
572C22×C4—124no—
573C22×C4—124no—
574C22×C4C23×D312yes—
575C22×C4C23×D312yes—
576C22×C4C23×D312yes—
577C22×C4C23×D311yescharacteristic
578C22×C4C23×D311yescharacteristic
579C22×C4C23×D311yescharacteristic
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—22no—
583C4⋊C4—34no—
584C4⋊C4—64no—
585C4⋊C4—64no—
586C4⋊C4—68no—
587C4⋊C4—68no—
588C4⋊C4—64no—
589C4⋊C4—64no—
590C4⋊C4—62no—
591C4⋊C4—64no—
592C4⋊C4—62no—
593C4⋊C4—62no—
594C4⋊C4—124no—
595C4⋊C4—122no—
596C4⋊C4—122no—
597C4⋊C4—124no—
598C4⋊C4—122no—
599C22⋊C4—24no—
600C22⋊C4—38no—
601C22⋊C4—44no—
602C22⋊C4—44no—
603C22⋊C4—64no—
604C22⋊C4—64no—
605C22⋊C4—68no—
606C22⋊C4—68no—
607C22⋊C4—68no—
608C22⋊C4—64no—
609C22⋊C4—68no—
610C22⋊C4—122no—
611C22⋊C4—124no—
612C22⋊C4—122no—
613C22⋊C4—124no—
614C22⋊C4—124no—
615C42—24no—
616C42—64no—
617C42—62no—
618C42—62no—
619C42—62no—
620C42—64no—
621C42#23714yes—
622C22×C3—24no—
623C22×C3—24no—
624C22×C3—24no—
625C22×C3—42no—
626C22×C3—42no—
627C22×C3—42no—
628C22×C3—42no—
629C22×C3—44no—
630C22×C3—44no—
631C22×C3—44no—
632C22×C3—44no—
633C22×C3—44no—
634C22×C3—44no—
635C22×C3—44no—
636C22×C3C23×D411yescharacteristic
637C22×C3C22×#4111yescharacteristic
638C22×C3C2×H(5,𝔽2)11yescharacteristic
639C22×C3C2×H(5,𝔽2)11yescharacteristic
640C22×C3C2×H(5,𝔽2)11yescharacteristic
641C22×C3C2×2−1+411yescharacteristic
642C22×C3#58511yescharacteristic
643C2×D3—22no—
644C2×D3—22no—
645C2×D3—22no—
646C2×D3—41no—
647C2×D3—41no—
648C2×D3—41no—
649C2×D3—41no—
650C3×C4—22no—
651C3×C4—42no—
652C3×C4—42no—
653C3×C4—42no—
654C3×C4#54014yescomplemented
655C3×C4#54714yes—
656Dic3—22no—
657Dic3—22no—
658Dic3—24no—
659Dic3—41no—
660Dic3—42no—
661Dic3—42no—
662Dic3—44no—
663Dic3—42no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—32no—
678C23—61no—
679C23—61no—
680C23—61no—
681C23—61no—
682C23—61no—
683C23—61no—
684C23C2×D3×D414yes—
685C23C24×D311yescharacteristic
686D4—28no—
687D4—48no—
688D4—48no—
689D4—84no—
690D4—88no—
691D4—88no—
692D4—128no—
693D4—248no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—32no—
706C2×C4—34no—
707C2×C4—32no—
708C2×C4—48no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—62no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—62no—
715C2×C4—68no—
716C2×C4—62no—
717C2×C4—62no—
718C2×C4—64no—
719C2×C4—61no—
720C2×C4—62no—
721C2×C4—61no—
722C2×C4—62no—
723C2×C4—61no—
724C2×C4—64no—
725C2×C4—62no—
726C2×C4—62no—
727C2×C4—62no—
728C2×C4—64no—
729C2×C4—62no—
730C2×C4—62no—
731C2×C4—124no—
732C2×C4—124no—
733C2×C4—248no—
734C2×C4—248no—
735C2×C4C2×D3×D412yes—
736C2×C4C2×#23712yes—
737C2×C4C2×#23712yes—
738C2×C4C2×#23712yes—
739C2×C4#100412yes—
740C2×C4#100412yes—
741C2×C4#101012yes—
742C2×C3—44no—
743C2×C3—84no—
744C2×C3C2×#54011yescharacteristic
745C2×C3C2×#54711yescharacteristic
746C2×C3#349411yescharacteristic
747C2×C3#349611yescharacteristic
748C2×C3#349811yescharacteristic
749C2×C3#354811yescharacteristic
750C2×C3#355411yescharacteristic
751D3—42no—
752C22—24no—
753C22—24no—
754C22—24no—
755C22—42no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—62no—
767C22—62no—
768C22—62no—
769C22—121no—
770C22—121no—
771C22—121no—
772C22—121no—
773C22C22×D3×D411yescharacteristic
774C22C22×#23711yescharacteristic
775C22C2×#100411yescharacteristic
776C22C2×#100411yescharacteristic
777C22C2×#101011yescharacteristic
778C22D3×H(5,𝔽2)11yescharacteristic
779C22#596611yescharacteristic
780C4—22no—
781C4—42no—
782C4—42no—
783C4—42no—
784C4—62no—
785C4—64no—
786C4—62no—
787C4—122no—
788C4—124no—
789C4—122no—
790C4—121no—
791C4—122no—
792C4#561114yes—
793C4#571914yescomplemented
794C3#3935211yescharacteristic, complemented, Sylow
795C2—44no—
796C2—84no—
797C2—122no—
798C2C2×#561111yescharacteristic
799C2C2×#571911yescharacteristic
800C2#8633211yescharacteristic
801C2#8660811yescharacteristic
802C2#8662111yescharacteristic
803C2#8678011yescharacteristic
804C2#8678911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D3
commutator, socle, cosocleC23×C3C25
FittingC3×#2541C2
hypercenter#2541D3
hypocenterC3#39352
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C23 ◁ #2541

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#5719C2semidirect
2. C3×#2541C2semidirect
3. #83192C2semidirect
4. #83176C2semidirect
5. #83173C2semidirect
6. #82705C2semidirect
7. #82667C2semidirect
8. #82664C2semidirect
9. #82644C2semidirect
10. C4×#938C2semidirect
11. D4×C4⋊Dic3C2semidirect
12. #76725C2semidirect
13. #76710C2semidirect
14. #76458C2semidirect
15. #76324C2semidirect
16. #73753C2semidirect
17. #73716C2semidirect
91. #2541D3semidirect
144. #938D4semidirect
654. C3×C4#540semidirect
793. C4#5719semidirect
794. C3#39352semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#57192
C3×#25412
#831922
#831762
#831732
#827052
#826672
#826642
#826442
C4×#9382
D4×C4⋊Dic32
#767252
#767102
#764582
#763242
#737532
#737162
#393523